ICPC WF Moscow Invitational Contest(Kingdom of Islands-枚举子集)

Posted 2022-02-02 nike0good

给$1$个$n\le 1e5$个点的图，每个点有权值$s_i$。若$2$个点$s_i$不同，则连边，否则不连边。
有$k\le 20$个特例：原来连边变成不连，或者不连变成连。
求最大完全子图

如果没有特例点，每个$s_i$取一个点即可。
考虑有特例的情况：
两个点从连边变成不连：枚举哪个点不在子图中
两个点从不连边变成连：枚举是否两个点都在子图中
剩下贪心

#include<bits/stdc++.h> 
using namespace std;
#define For(i,n) for(int i=1;i<=n;i++)
#define Fork(i,k,n) for(int i=k;i<=n;i++)
#define ForkD(i,k,n) for(int i=n;i>=k;i--)
#define Rep(i,n) for(int i=0;i<n;i++)
#define ForD(i,n) for(int i=n;i>0;i--)
#define RepD(i,n) for(int i=n;i>=0;i--)
#define Forp(x) for(int p=pre[x];p;p=next[p])
#define Forpiter(x) for(int &p=iter[x];p;p=next[p])  
#define Lson (o<<1)
#define Rson ((o<<1)+1)
#define MEM(a) memset(a,0,sizeof(a));
#define MEMI(a) memset(a,0x3f,sizeof(a));
#define MEMi(a) memset(a,128,sizeof(a));
#define MEMx(a,b) memset(a,b,sizeof(a));
#define INF (0x3f3f3f3f)
#define F (1000000007)
#define pb push_back
#define mp make_pair
#define fi first
#define se second
#define vi vector<int> 
#define pi pair<int,int>
#define SI(a) ((a).size())
#define Pr(kcase,ans) printf("Case #%d: %lld\\n",kcase,ans);
#define PRi(a,n) For(i,n-1) cout<<a[i]<<' '; cout<<a[n]<<endl;
#define PRi2D(a,n,m) For(i,n)  \\
						For(j,m-1) cout<<a[i][j]<<' ';\\
						cout<<a[i][m]<<endl; \\
						 
#pragma comment(linker, "/STACK:102400000,102400000")
#define ALL(x) (x).begin(),(x).end()
#define gmax(a,b) a=max(a,b);
#define gmin(a,b) a=min(a,b);
typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;
ll mul(ll a,ll b)return (a*b)%F;
ll add(ll a,ll b)return (a+b)%F;
ll sub(ll a,ll b)return ((a-b)%F+F)%F;
void upd(ll &a,ll b)a=(a%F+b%F)%F;
inline int read()

	int x=0,f=1; char ch=getchar();
	while(!isdigit(ch)) if (ch=='-') f=-1; ch=getchar();
	while(isdigit(ch))  x=x*10+ch-'0'; ch=getchar();
	return x*f;
 
#define MAXN (100000+10)
 
#define MAXM (21)
int P,n;
int s[MAXN];
int c[MAXN];
int k;
int u[MAXM],v[MAXM];
map<pair<int,int>,int > h;
bool check(vi v,vi ban) 
	int sz=SI(v);
	Rep(i,sz) Fork(j,i+1,sz-1) 
		int x=v[i],y=v[j];
//		cout<<(s[x]!=s[y])<<' '<<(h.count(mp(x,y))) <<endl;
		if((s[x]!=s[y]) ==(h.count(mp(x,y))>0) ) return 0;
	
	return 1;

int t_ck[MAXN]=,clo=0;
bool is_ck[MAXN]=;
bool is_ban[MAXN]=;
 
int main()

//	freopen("k.in","r",stdin);
//	freopen(".out","w",stdout);
//  cin.tie(0)->sync_with_stdio(0); 
	P=read(),n=read();
	For(i,n) s[i]=read(),c[s[i]]++;
	k=read();
	Rep(i,k) u[i]=read(),v[i]=read(),h[mp(u[i],v[i])]=h[mp(v[i],u[i])]=1;
	int S=1<<k;
	int ans=0;
	vi ex1,ba1;
	Rep(st,S) 
		vi exist,ban;
		++clo;
		Rep(i,k) 
			bool fl=(st>>i)&1;
			int u=::u[i],v=::v[i]; 
			if(s[u]==s[v]) 
				if(fl) 
					exist.pb(u);
					exist.pb(v);				
					t_ck[u]=t_ck[v]=clo;
				
			else 
				if(fl) 
					ban.pb(u);
				else ban.pb(v);
			
		
		sort(ALL(exist));
		exist.erase(unique(ALL(exist)),exist.end() );
		sort(ALL(ban));
		ban.erase(unique(ALL(ban)),ban.end() );
		
		bool flag=0;
		for(auto p:ban) if(t_ck[p]==clo) flag=1;break;
		if(flag) continue;
		else if(!check(exist,ban)) continue;
		else 
			int z=0;
			for(auto x:exist) 
				int p=s[x];
				if(c[p]>0) ++z;
				c[p]-=1e7;
			
			for(auto x:ban) 
				int p=s[x];
				--c[p];
				z+=c[p]==0;
			
			z=SI(exist)+P-z;
			if(ans<z) 
				ans=z;
				ex1.assign(exist.begin(),exist.end());
				ba1.assign(ban.begin(),ban.end());
			
//			ans=max(ans,z);
			for(auto x:ban) 
				int p=s[x];
				++c[p];
			
			for(auto x:exist) 
				int p=s[x];
				c[p]+=1e7;
			
 
		
	
	cout<<ans<<endl;
	for(auto x:ex1)
		is_ck[s[x]]=1;
	
	for(auto x:ba1) 
		is_ban[x]=1;
	
	For(i,n) if(!is_ban[i] && is_ck[s[i]]==0) 
		is_ck[s[i]]=1;
		ex1.pb(i);
	
	int sz=SI(ex1);
	Rep(i,SI(ex1)) 
		cout<<ex1[i];
		putchar(i<sz-1?' ':'\\n');
	
//	for(auto x:ex1) cout<<x<<' ';
	return 0;